

where \(\delta _i\)  is the internal voltage phase angle; \(\omega _i\)  is frequency; \(P_{\text{G}i}\)  is the instantaneous real power component [1]}; \(P_i\)  is the real power filtered by the digital filter; \(\omega _{\text{c}i}\)  is the cut-off frequency of the digital filter; \(\omega _{\text{s}i}\)  is the setpoint; and \(m_{\text{P}i}\)  is the droop coefficient. Equation (REF ) is introduced by definition; and Equations () and () are resulting from the digital filter dynamics and the droop characteristic [1]}. Variables \(P_{\text{G}i}\) , \(P_i\) , \(\delta _i\) , and \(\omega _{\text{s}i}\)  are annotated in Figure REF .
Since \(\omega _i\)  is the variable that is regulated by the \(\mu \) AGC, we eliminate \(P_i\)  by noting
\( \dot{\omega }_i = -m_{\text{P}i} \dot{P}_i; \quad P_i = (\omega _{\text{s}i}- \omega _i)/m_{\text{P}i}.\) 
